Let's solve the problem step-by-step:

Part (a): Theoretical Probability of Getting a 4

The machine outputs numbers from 0 to 9, so there are 10 possible outcomes. Assuming the machine is fair, each number has an equal probability of being picked.

$P(\text{getting a 4}) = \frac{1}{\text{total outcomes}} = \frac{1}{10} = 0.1$

Thus, the theoretical probability of getting a 4 is 0.1 or 10%.

Part (b): Experimental Probability of Getting a 4

From the table:

• The number of trials = 100
• The number of times a 4 was chosen = 13

The experimental probability is calculated as:

$P_{\text{experimental}} = \frac{\text{Number of times 4 was chosen}}{\text{Total number of trials}} = \frac{13}{100} = 0.13$

Thus, the experimental probability of getting a 4 is 0.13 or 13%.

Part (c): Correct Statement

The correct statement is:

"The larger the number of trials, the greater the likelihood that the experimental probability will be close to the theoretical probability."

This is because as the number of trials increases, the law of large numbers ensures that the experimental probability approaches the theoretical probability.

Final Answers:

(a) Theoretical probability = 0.1
(b) Experimental probability = 0.13
(c) Correct statement = "The larger the number of trials..."

Let me know if you need further clarification!

Related Questions:

1. How do we calculate theoretical probability for more complex cases?
2. What is the law of large numbers, and how does it affect probability results?
3. How would the probabilities change if the machine was biased?
4. What is the difference between experimental probability and theoretical probability?
5. How can we check if a machine like this is fair?

Tip: Experimental probability becomes more accurate as the number of trials increases. Always compare experimental results with theoretical expectations to detect biases.